What is Potential energy: Definition and 998 Discussions
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.
The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, and does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work.
Is gravitational potential energy defined only for internal conservative forces?
For reference, this is the chapter.
Suppose we have two objects: object 1 and also object 2.
If we consider the system to be both objects, then we can compute the work done by the pair of internal conservative...
Hello! Apologies if I'm missing some information but here is my thinking so far. Had the drag force not been there, the potential energy would equal the amount of energy the explosives have to disipate to get the car to that height. However, since drag force is included it makes it more...
Can I understand the relationship between binding energy and mass by comparing it to the relationship between kinetic energy and potential energy?
When an object falls, its gravitational potential, a scalar value, decreases, and its energy is converted into kinetic energy. Even when a nuclear...
One solution is that if we move with the same velocity as the spring does, the initial velocity of the block will be ##v## and the final will be zero, so its kinetic energy will transform into a potential energy of the spring.
I would also say that we can say that if we pull the spring, we...
The system of two material points of identical mass connected by a rigid rod of negligible mass and length ##L## is an example of a conservation of energy problem. The initial energy of the system is the sum of the kinetic energy of the two points and the potential energy of the rod, which is...
Good afternoon,
I have a question on graphing this problem. There seems to be something weird going on.
In Excel, I set up the potential energy function (kx²/2) and plotted it from x = -0.300m to 0.300m, which looks like the following:
The overall shape of the graph looks like what's...
Max speed occurs when all energy has been translated from spring into box.
E (Potential) = 1/2kx^2
E (Potential) = (1/2)(42 N/m)(0.280 m)^2 = 1.6464 N m
Ep = Ek =1/2mv^2
1.6464 N m= 1/2 (1.2 kg) v^2
v = 1.6565 m/s
I might be getting hooked up on this subject, but this is the last question I'm gonna ask about this.
When potential energy on earth is given by ##mgy##, we know space is said to be homogeneous. If you're standing on the ground and in one case, ball is dropped from some height and then another...
Why there will be no change in potential energy due to this sharp blow ? Potential energy is a function of position , so won't this position get changed due to this sharp blow?Please help!
I have found some papers (like this one: https://www.aanda.org/articles/aa/full_html/2009/45/aa12762-09/aa12762-09.html) which say that dark energy increases the potential energy in a system of a quasi-stationary gravitationally bound many-body system.
It also says that because of this, the...
In the chapter of center of mass and linear momentum, there are multiple problems involving two block systems connected by a string, with both blocks given certain initial velocities. The goal is to calculate the maximum elongation or compression in the spring.
For example, consider this...
Hi,
Am i correct in thinking that if we take a block of ice, moving at a constant velocity, it's then exposed to a heat source which melts the ice and turns it into water vapour, that we have simply removed any Kinetic energy, by Sublimation or converting it into heat.
My question is does the...
I'm a diving coach at the local YMCA and I want to give a lesson regarding the physics of diving off the board with maximum efficiency. This is the type of diving board with an adjustable fulcrum, basically a lever with one end fixed with bolts. Its been almost 15 years since I've taken a...
Hello everybody, I consider two electrons that have enough kinetic energy to reach their respective classical electron radius. This would be:
2.0514016772310431402e-13 J
The corresponding speed is v = 287336682 m/s.
The electric field is
E = \frac{k_{e}}{R_e^2} = 1.8133774657059088443 ×...
I got answer for (a), which is 0.51 m
For (b), loss of potential energy = 35 x 9.81 x 0.51 = 175 J
Rate of loss of potential energy = 175 J / 1 s = 175 W
But the answer key is 80 W. Where is my mistake?
Thanks
When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?
W_ext is the external work done on B and C, which is 12 J
Delta K_tot is the internal work, which is the work done by A on B plus the work done by A on C
Delta K_tot = 5
Solving for \Delta U, we find that the change in potential energy is 7 J
This answer says otherwise...
Hello,
so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##.
I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...
"Heat is the transfer of kinetic energy between molecules. If the velocity is more, the kinetic energy will be more so that the heat is more."
"As an object's speed increases, the drag force from the fluid increases exponentially. For example, when you drive at high speeds, the frictional force...
Since the forces involved (gravity and electric force) are conservative we can use conservation of energy.
The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
Ki + Ui = Kf + Uf
1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so
1/2)kx^2 = F∆d.
The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.
I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...
Hi, Everyone! This is the page(first image) from Principle of physics by resnik.
I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition?
Secondly, how did they reach...
If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2?
I...
Suppose there is a pressurized gas canister in space, at rest. With a mass "m" of gas inside of it at a pressure "P".
Next the valve of the canister is opened. The canister will accelerate in the opposite direction to the valve opening. When all the gas has left the canister, it will be moving...
While reading this thread on Stack Exchange... https://physics.stackexchange.com/questions/113092/why-does-a-system-try-to-minimize-potential-energy ... a question came to mind : -
Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end...
Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...
My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...
In generic terms and expressions without going into specificity or nature of fields/forces in order to highlight the same, how exactly could we characterise the distinction between 'Potential' & 'Potential Energy'?
Suppose a charged particle is in an electric field and feels an electric potential. Then the particle travels through a wormhole to another electric field and the particle feels a different electric potential. The potential energy of the particle will change. So what will that part of potential...
I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning:
1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2).
2) F= stress/area. Force (load is the same). If cross sectional area...
Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of...
Hi, if the force is the derivative of potential energy, does it mean that the force is equal to mg and with a constant gravity, it will be the same at any height?
But in real life, F (or mg) would be different on the Earth's surface and 400 km above it (~8 m/s^2).
So, this formula is used to...
Suppose I have some interaction potential, u(r), between two repelling particles. We will name them particles 1 and 2.
I want to find the force vectors F_12 and F_21. Would I be correct in saying that the x-component of F_12 would be given by -du/dx, y-component -du/dy etc? And to find the...
So the potential energy of an object in a gravitational field is pe=hmg where h is the height of the object in the gravitational field in meters m is the mass in kilograms and g is the acceleration in meters per second per second
I read on an answer to a question that the force to lift an...
I'm stuck in a problem of a spring mass system with a pendulum attached to it as showed in the figure below:
My goal is to find the movement equation for the mass, using Lagrangian dynamics.
If the spring moves, the wire will move the same amount. Therefore, we can write the x and y position...
Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force.
The weight is simple enough ##12* 9.8=117.6N##...
Summary:: A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying 40kg of gear. How much power does he need to reach the top of the building in 55s.
So first the total mass of our system is 130 kg. Using this mass, I found the potential energy the firefighter would...
The energy stored in a capacitor is derived by integrated the work needed to move charge dQ from one plate to another. I'm confused on how this energy is the same as electrostatic potential energy, the energy needed to assemble this configuration from infinity. In the case of capacitor energy...
I thought the largest PE difference would be when the loop's area vector is in the same direction as the magnetic field, hence cos(0) =1, minus when the loop's area vector in perpendicular to the field, cos(pi/2) = 0. Just plug in the variables and you get 0.126 joules. Did I make a mistake?
There are six pairs. three turn out to be negative and three turn out to be positive (3q^2 - 3q^2) which nets zero when you add them together with the equation. But zero was the incorrect answer. Did I do something wrong? Thank you
We can find the potential energy by finding the potential difference between the two masses. the minimum distance between the two masses is 10 cm. The maximum is 30 cm because they can be 3 string lengths apart as they repulse each other once the string is cut.
So, to get potential difference...
Hello everyone, I'd like to share a doubt I am currently struggling with.
So we know that ΔU=−W, where ΔU is the difference of potential energy and Wthe work done by the force to move the body from point A to point B.
When analyzing this for the gravitational force, since we have U=−GmM/R, with...
##T-2mg=2ma_1## (acceleration of heavier mass)
##T-mg=ma_2##
(##-a_1=a_2##)
On solving the eqns, ##a_1=-g/3=-a_2##
##s=1/2at^2##
##s=-g/6## , distance covered by heavier mass.
##s=g/6## , covered by lighter mass.
Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass)
##\Delta...
Summary:: I have been trying to do this question for a while using the hydrostatic relationship to put rho and z in terms of p, however, I can not seem to end up with an answer. Can anyone suggest where to start.
The question is as follows:
Air is heated in a vertical piston–cylinder assembly fitted with an electrical resistor. The volume of the air slowly increases by 1.6 ft^3 while its pressure remains constant. The area of the piston is 1 ft^2. The mass of the air is 0.6 lb. The local acceleration of gravity is g = 32.0 ft/s^2...
In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$
Terms in...
Ion traps are very complex, but one of my Physics Olympiad textbooks presents a simplified model of a resonating charged particle in an ion trap
A tuned circuit consists of an inductor and a parallel plate capacitor (capacitance C and plate separation d). It has a resonating frequency ##\nu...
I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help.
The torque on a dipole can be defined as
τ=PEsinθ
The work done on a dipole to move it from an angle ##\theta_0##...